重新审视基于搜索的复杂性分析：新的计算技术和改进的边界
Revisiting the Complexity Analysis of Conflict-Based Search: New Computational Techniques and Improved Bounds
摘要：
多智能体路径查找（MAPF）问题要求在给定的环境中为一组智能体找到一组无冲突的路径。可以说，计算最优解的最先进方法是基于搜索的搜索（CBS）。在这项工作中，我们重新审视CBS的复杂性分析，在最坏的情况下，算法的运行时间提供更严格的界限。我们的分析铺平了道路，以更好地查明参数，治理（在最坏的情况下）的算法的计算复杂性。我们的分析是基于两种互补的方法：在第一种方法中，我们绑定的运行时使用的多值决策图（MDD）的大小-一个分层的图，其中包含所有可能的单代理路径之间的两个给定的顶点为一个特定的路径长度。在第二种方法中，我们表示的运行时间由一个新的递归关系的边界算法的复杂性。我们使用基于生成函数的分析，以紧密结合的递归。使用这些技术，我们提供了几个新的上限CBS的复杂性。结果使我们能够改善现有的约束CBS的运行时间在许多情况下。例如，在一组常见的基准测试中，我们将上限至少提高了$2^{10^{7}}$。
英文摘要：
The problem of Multi-Agent Path Finding (MAPF) calls for finding a set of conflict-free paths for a fleet of agents operating in a given environment. Arguably, the state-of-the-art approach to computing optimal solutions is Conflict-Based Search (CBS). In this work we revisit the complexity analysis of CBS to provide tighter bounds on the algorithm's run-time in the worst-case. Our analysis paves the way to better pinpoint the parameters that govern (in the worst case) the algorithm's computational complexity. Our analysis is based on two complementary approaches: In the first approach we bound the run-time using the size of a Multi-valued Decision Diagram (MDD) -- a layered graph which compactly contains all possible single-agent paths between two given vertices for a specific path length. In the second approach we express the running time by a novel recurrence relation which bounds the algorithm's complexity. We use generating functions-based analysis in order to tightly bound the recurrence. Using these technique we provide several new upper-bounds on CBS's complexity. The results allow us to improve the existing bound on the running time of CBS for many cases. For example, on a set of common benchmarks we improve the upper-bound by a factor of at least $2^{10^{7}}$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
